Simplify the following expression: $\dfrac{18z^4}{54z^2}$ You can assume $z \neq 0$.
Answer: $ \dfrac{18z^4}{54z^2} = \dfrac{18}{54} \cdot \dfrac{z^4}{z^2} $ To simplify $\frac{18}{54}$ , find the greatest common factor (GCD) of $18$ and $54$ $18 = 2 \cdot 3 \cdot 3$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $ \mbox{GCD}(18, 54) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{18}{54} \cdot \dfrac{z^4}{z^2} = \dfrac{18 \cdot 1}{18 \cdot 3} \cdot \dfrac{z^4}{z^2} $ $\phantom{ \dfrac{18}{54} \cdot \dfrac{4}{2}} = \dfrac{1}{3} \cdot \dfrac{z^4}{z^2} $ $ \dfrac{z^4}{z^2} = \dfrac{z \cdot z \cdot z \cdot z}{z \cdot z} = z^2 $ $ \dfrac{1}{3} \cdot z^2 = \dfrac{z^2}{3} $